Finite Group Databasebeta

← #14671317

Subgroups — #14671317

Order 2816.

752 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072231C211yesmaximal, characteristic
2C2×#10622115C212yesmaximal, complemented
3#13068544C211yesmaximal, characteristic, complemented
4#13066742C212yesmaximal, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×M16—21no—
8C2×#67000C2211yescharacteristic
9C2×#66993C411yescharacteristic
10C2×#66983C411yescharacteristic
11C11×#413—24no—
12C2×C11×#101C2212yes—
13C2×C11×#100—21no—
14#10622843C2211yescharacteristic
15C2×#66900C2212yes—
16#10622836—21no—
17#10622836—21no—
18#10622834C411yescharacteristic
19C2×#66897—21no—
20#10622826—21no—
21#10622826—21no—
22C4×C22⋊Dic11C411yescharacteristic
23#10622820—21no—
24#10622115—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C22×Q8×C11C2311yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×C22⋊D11—21no—
38C22×C22⋊D11—21no—
39C22×C22⋊D11—21no—
40C22×D44C2×C411yescharacteristic
41C2×C11×M16—24no—
42C2×C11×M16—22no—
43C2×C11×M16—42no—
44C2×C11×M16—41no—
45C22×C8×C11—41no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49#67000—22no—
50#67000—22no—
51#66993—42no—
52#66983—41no—
53#66983—41no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4×Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C411yescharacteristic
60C2×#4318—22no—
61C11×#101—22no—
62C11×#101D414yescomplemented
63C11×#100—24no—
64#66900—22no—
65#66900—22no—
66#66897—42no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13093—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C23×D11—21no—
77C11×#41—44no—
78C11×#41—44no—
79C11×#41—44no—
80C11×#41—44no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11C2×D412yes—
84C2×Q8×C11#4112yes—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—42no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—42no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—81no—
118C2×C22⋊D11—81no—
119C2×C22⋊D11—81no—
120C2×C22⋊D11—81no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C2×D44—22no—
125C2×D44—41no—
126C2×D44—41no—
127C11×M16—24no—
128C11×M16—44no—
129C11×M16—42no—
130C2×C8×C11—44no—
131C2×C8×C11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—81no—
134C22⋊Dic11—81no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—41no—
141C4×Dic11—22no—
142C4×Dic11—41no—
143#4318—42no—
144#4318—42no—
145C2×C11⋊C8—42no—
146C2×#413D1111yescharacteristic, complemented
147#2431—111no—
148C2×#355—112no—
149#1785—111no—
150#1394—112no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#9912yes—
166C23×C11C2×C22⋊C411yescharacteristic
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174Q8×C11—42no—
175Q8×C11—42no—
176D4×C11—44no—
177D4×C11—44no—
178D4×C11—42no—
179D4×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11#9911yescharacteristic
197C2×C4×C11#9911yescharacteristic
198C2×C4×C11C4×D412yes—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12112yes—
201C2×C4×C11#12311yescharacteristic
202C22⋊D11—84no—
203C22⋊D11—84no—
204C22⋊D11—84no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214D44—82no—
215C8×C11—44no—
216C11⋊C8—82no—
217C22×#41C2×D1111yescharacteristic
218C22×M16—21no—
219C2×#127—111no—
220C2×#124—111no—
221C2×#121—111no—
222#413—24no—
223C2×#101—112no—
224C2×#101C2×D1112yes—
225C2×#100—21no—
226C2×#100—221no—
227#407—221no—
228#392—221no—
229#392—221no—
230#391—111no—
231#390—111no—
232#386—221no—
233#386—221no—
234C4×C22⋊C4—111no—
235#355—224no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—22no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11#38611yescharacteristic
254C22×C11C2×#9911yescharacteristic
255C22×C11C2×#9911yescharacteristic
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C2×D11—81no—
261C2×D11—81no—
262C2×D11—81no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—22no—
268C4×C11—22no—
269Dic11—42no—
270Dic11—81no—
271Dic11—81no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—41no—
275C2×#41—41no—
276C2×#41—42no—
277C22×Q8C22×D1111yescharacteristic
278C22×D4—111no—
279C22×D4—221no—
280C22×D4—221no—
281C22×D4—221no—
282C22×D4C4×D1111yescharacteristic
283C22×D4D4411yescharacteristic
284C22×D4C22⋊D1111yescharacteristic
285C23×C4C4×D1111yescharacteristic
286C23×C4D4411yescharacteristic
287C23×C4C22⋊D1111yescharacteristic
288C2×M16—24no—
289C2×M16—22no—
290C2×M16—42no—
291C2×M16—41no—
292C2×M16—222no—
293C22×C8—41no—
294#127—442no—
295#124—222no—
296#124—222no—
297#121—441no—
298#121—441no—
299C2×C4⋊C4—111no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C22⋊C4—221no—
304C2×C22⋊C4—221no—
305C2×C22⋊C4—221no—
306C2×C42—111no—
307C2×C42—111no—
308#101—22no—
309#101—222no—
310#101—222no—
311#101C22⋊D1114yescomplemented
312#100—24no—
313#100—442no—
314C22⋊C8—441no—
315C22⋊C8—441no—
316#95—221no—
317#95—221no—
318#95—221no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—42no—
322C2×C11—81no—
323C2×C11—81no—
324C2×C11#189811yescharacteristic
325C2×C11#213211yescharacteristic
326C2×C11#213411yescharacteristic
327D11—161no—
328C24—221no—
329C24(C2×D11)⋊C411yescharacteristic
330C24(C2×D11)⋊C411yescharacteristic
331C24(C2×D11)⋊C411yescharacteristic
332#41—44no—
333#41—44no—
334#41—44no—
335#41—44no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8#433912yes—
339C2×Q8C2×C22⋊D1112yes—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—222no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—442no—
357C2×D4—442no—
358C2×D4—881no—
359C2×D4—881no—
360C2×D4—881no—
361C2×D4—881no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4(C2×D11)⋊C411yescharacteristic
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4C2×D4411yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382M16—24no—
383M16—44no—
384M16—42no—
385M16—442no—
386M16—442no—
387C2×C8—44no—
388C2×C8—42no—
389C2×C8—442no—
390C4⋊C4—441no—
391C22⋊C4—442no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—442no—
396C22⋊C4—441no—
397C22⋊C4—881no—
398C22⋊C4—881no—
399C42—222no—
400C42—441no—
401C11#1309311yescharacteristic, complemented, Sylow
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23#6687012yes—
424C23C2×(C2×D11)⋊C411yescharacteristic
425Q8—42no—
426Q8—42no—
427D4—44no—
428D4—44no—
429D4—42no—
430D4—42no—
431D4—882no—
432D4—884no—
433D4—884no—
434D4—884no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—222no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4#6687011yescharacteristic
461C2×C4#6687011yescharacteristic
462C2×C4C4×C22⋊D1112yes—
463C2×C4#6698211yescharacteristic
464C2×C4#6698312yes—
465C2×C4#6700611yescharacteristic
466C8—44no—
467C8—882no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—881no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22—881no—
492C22C2×#6687011yescharacteristic
493C22C2×#6687011yescharacteristic
494C22#1062282611yescharacteristic
495C4—21no—
496C4—22no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—442no—
502C4—881no—
503C4—881no—
504C2—21no—
505C2—21no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—1761no—
510C2#1306906911yescharacteristic
511C2#1307029911yescharacteristic
512C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#413C2
socleC22×C11C2×#99
prime radical#13072231C2
cosocleC22×Q8×C11C23
hypercenterC2×#413D11
hypocenterC11#13093
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622115C2semidirect
3. #13068544C2semidirect
4. #13066742C2semidirect
5. C2×C11×#413C2semidirect
62. C11×#101D4semidirect
146. C2×#413D11semidirect
311. #101C22⋊D11semidirect
401. C11#13093semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130722312
C2×#106221152
#130685442
#130667422
C2×C11×#4132
#1309311